论文标题
Quillen的猜想通过等效式式技术的一些结果
Some results on Quillen's Conjecture via equivalent-poset techniques
论文作者
论文摘要
我们将Aschbacher和Smith的主要定理扩展到Quillen的猜想中，从$ p> 5 $扩展到剩余的奇数$ P = 3,5 $。在此过程中，我们开发了进一步的组合和同位方法来研究有限群体的非平凡基本Abelian $ p $ -subgroups。这些技术导致了对猜想的进一步结果，通常会降低对CFSG的依赖。特别是，我们还为$ p = 2 $的情况提供了一些部分结果。
We extend the Main Theorem of Aschbacher and Smith on Quillen's Conjecture from $p>5$ to the remaining odd primes $p = 3,5$. In the process, we develop further combinatorial and homotopical methods for studying the poset of nontrivial elementary abelian $p$-subgroups of a finite group. The techniques lead to a number of further results on the Conjecture, often reducing dependence on the CFSG; in particular, we also provide some partial results toward the case of $p=2$.
